Passive ranging system

ABSTRACT

Range and velocity of target vehicles are determined from the angles of arrival of strobes from the target vehicles to provide a completely passive, linear, ranging system. From inputs which include strobe angle, time of strobe and receiving vehicle cross range position, the targets vehicles ranges and velocities are determined. A visual presentation is provided to enhance detecting the target vehicle in a high density environment.

BACKGROUND

1. Field

The present invention relates to passive ranging systems and, moreparticularly, to such systems in which angular position information isthe only data obtained from the target.

2. Prior Art

Radar surveillance aircraft are often faced with the problem ofoperating in a dense and moving environment. The radar displays aboardthe surveillance aircraft are adversely affected by jamming sources, butmay be restored by locating these jamming sources. It is preferable toaccomplish the location of the jamming sources passively from thesurveillance aircraft to reduce the probability of detection and toavoid the need for cooperating aircraft or ground stations in locatingthe jammers.

A number of triangulation techniques are available; however,surveillance aircraft generally do not provide sufficient distancebetween direction finding antennas to make use of these techniques.

A first prior art nontriangulation technique uses the fact that theintercepted power from a target vehicle is proportional to the inverseof the range squared. Hence, two surveillance aircraft carryingintercept receivers separated by a substantial distance along the linedirected at the jammer will measure slightly different interceptedpowers which may be used (environment permitting) to calculate range.However, the required separation in receivers does not permit thistechnique to be carried out with a single aircraft.

A second prior art technique uses the elevation angle of the interceptand an assumed value of the jammer altitude to calculate range. Thistechnique, like the first, is very sensitive to propagation andequipment errors and is based on an altitude assumption which greatlyreduces it reliability.

A third scheme is similar to the second, except that the jammer groundreflection is used to obtain an estimate of elevation angle. Thetime-difference or phase-difference-of-arrival of the direct and groundbounce intercepted signals is computed, and this information (convertedto jammer elevation angle) together with the target altitude assumption,is used to calculate range. The continued use of the altitutdeassumption again makes this scheme unreliable.

A fourth technique is a further variant which uses the bistatic radarreflection off a nonradiating target caused by a cooperative ornoncooperative ground surveillance radar. The time-difference-of-arrivalbetween the direct surveillance radar intercept and the bistaticreflection from a target places the target on an ellipsoid of which thesurveillance radar transmitter and the intercept receiver are foci. Ifthe target-bearing angle can be determined using the intercept antenna,the target may then be located on a line which is the intersection ofthe bearing angle plane with the ellipsoid. If, further, the jammeraltitude can be estimated, the intersection of the aforementioned linewith the plane of constant altitude determines jammer position. Again anassumed altitude is used making this technique unreliable. In addition,a cooperating or noncooperating ground surveillance radar is required.

Two other techniques that apply to airborne emitters bear mentioning.The first is ground imaging of the area directly underneath the emitterby comparing the ground-reflected intercept energy with thedirectly-received intercepted energy which is used as a reference. Thejammer position is then determined by comparing the image obtained fromthe intercept with aerial photographs or images obtained by other means.This requires appreciable time which is rarely, if ever, available in acombat situation.

Another technique is called PROSE, for Passive Ranging On ScanningEmitters. This technique is applicable to ranging on an enemy AWACS-likeemission: that is, the emission from a scanning radar in place of thejammers or jammer-like sources considered above. In this case, the enemyradar scan rate can be measured rather accurately using the averageinterval between main lobe intercepts determined over a long time base.If then two intercept antennas are provided on the friendly surveillanceaircraft, and the time delay between corresponding main beam interceptson these two antennas is calculated rather accurately, the parallaxangle, or angle of rotation of the enemy scanning radar, between theintercepts at the two antennas can be calculated. Then, knowing thedistance between the two intercept antennas, the range to the enemyscanning radar from the friendly surveillance aircraft can becalculated. Although this approach is a parallax-like technique, itrequires a large aperture for the scanning radar antenna and a longbaseline, neither of which may be available.

A typical passive ranging scenario is shown in FIG. 7. As noted above,the traditional problem is to obtain the range of an unfriendly emittingtarget using angle of arrival information obtained via a directionalreceiver onboard a friendly vehicle. FIG. 7 shows a first flight path701 of a jamming aircraft, a second flight path 702 of a surveillanceaircraft, first, second and third segment of the surveillance flightpath designated by drawing numeral 703, 704 and 705, respectively, acorresponding first, second and third segment of the jammer flight pathdesignated by drawing numerals 709, 710 and 711, respectively, andstrobes connecting the respective centers of the first, second and thirdsegments of the two flight paths, designated by drawing numerals 706,707 and 708. To aid in distinguishing the three different flight pathsegments and their respective strobes, a dotted line has been used forthe first, a dashed line for the second and a solid line for the third.

Accordingly, in FIG. 7, three jammer bearing angles are shown: the firstdotted, the second dashed, and the third in solid. The correspondingsegments of the jammer and surveillance flight paths are shown indotted, dashed and solid line coding. If the jammer had been fixed, thethree strobes would intersect in a point when projected back from theknown locations of the surveillance aircraft at the time the strobeswere received. The back projection of the strobes would intersect at theestimated position of the fixed jammer. The case that is shown, however,is for a moving jammer. The conventional approach is based upon theassumption that the tangential component of jammer velocity is constant.When jammer tangential acceleration is much smaller than the radartangential acceleration component (as when the surveillance aircraft isflown in an arc), and the time intervals are equal, range is estimatedby locating the position in range (which is along the X-axis, 712 inthis Figure) for which the strobes are equally spaced and correctlyordered in cross range (which is along the Y-axis 715 in this Figure).The effect of radial component of jammer motion is small, as it causesonly a slight error in the estimated range of the jammer. This approach,however, depends strongly upon the identification of each strobe with aparticular unique jammer.

In FIG. 8, a second jammer has been added. This jammer is moving on apath 801 in an opposite direction to the first 701 and is located at adifferent range from the surveillance aircraft. Again, the new jammerstrobes are coded in accordance with the position of the radar andjammer at the time of the observation. Thus, the first strobe on eachjammer is coded by dotted lines 706 and 806, the second by dashed lines707 and 807, and the third by solid lines 708 and 808, as in theprevious Figure.

This Figure shows that if the radar operator is unable to identify aparticular jamming strobe with a particular jammer (as, for example,when both jammers are wide band noise of identical parameters), uniquejammer ranging may not be possible. For example, if the wrong dashedstrobe is assumed to be identified with the second jammer, its rangewould be incorrectly estimated as being about half-way between the twoactual jammer positions.

The problem then is how to estimate jammer positions unambiguouslywithout the need for identification of a particular strobe with aparticular jammer.

An approach to the solution of the problem involves the use of amodified form of a technique that has been in use recently in the fieldof modern X-ray technology. This technique, called Computer AugmentedTomography (CAT) X-ray, has been well developed for mapping continuouslydistributed emitters or absorbers using angle measurements only. The CATapproach, unfortunately, works only with a fixed object (emitter orabsorber). However, a review of this technique as it presently isapplied to fixed objects is necessary to understand any modificationswhich would make it applicable to the solution. In order to do this, areview of least means (LMS) ranging will be presented first.

FIG. 9 shows a typical radar flight path 901 in dashed lines and threeangle of arrival strobes 902, 903 and 904 in dotted lines that would beobtained on a single fixed jammer 907 (circle). LMS ranging defines oneof the three strobes as a reference and calculates the perpendiculardistance from the reference strobe to each of the other two at aparticular value of range (X). As an example, the two short dotted lines905 and 906 are the perpendicular distances that would be obtained for avalue of X somewhat shorter than the true range of the jammer. In LMSranging, the length of the two short dotted lines are squared and thensummed, and X is varied until a minimum value is found for the sum. Thiscondition would obviously be obtained when the test value of X was equalto the range of the jammer. In fact, even if the strobe positions werein error due to errors in the angle of arrival measuring system or inthe supposedly known position of the surveillance aircraft at the timeof the measurements, the LMS approach would give the optimum estimate ofthe range of a single jammer.

When a second jammer is added, however, unless the strobes can be keptseparate--that is, identified uniquely with a particular jammer, LMSranging would give a single jammer range estimate which is midwaybetween the two jammers.

The example is shown in FIG. 10. The second jammer 1007 has angle ofarrival strobes 1002, 1003 and 1004 in solid lines, and theperpendicular distances that correspond to the LMS estimate of range atthe ends of the callout lines 1005 and 1006 formed of alternate dots andlong dashes. This approach obviously does not work for multiple jammers.

CAT ranging, on the other hand, as it is applied to X-raying, may beimmediately applied to fixed jammers. The technique works by generatingfor each jamming strobe a weighted back projection which is weightedmost strongly (that is, brightest on a display system) at the measuredangle of arrival of the jammer strobe and which fades in intensitycorresponding to the potential accuracy of the angle of arrivalinformation. As an example, if the angle of arrival sensing system isknown to be accurate to about 5 degrees, the back projection would beweighted to have half intensity 5 degrees away from the measured angleof arrival of the received jammer signal.

Jammer positions would now be estimated by overlaying back projectionscorresponding to each of the three jammer strobe positions of theprevious illustration.

FIG. 11 shows what would happen if the strobes were presented on acathode-ray tube display with one jammer where the back projections wereunweighted. Notice that the three strobes 1102, 1103 and 1104 on thedisplay are brightest in the area designated by drawing numeral 1105where the strobes overlay one another which is only at the estimatedposition of the jammer. These strobes are of equal, moderate intensity.Where they all cross, the intensities add, and a bright white area 1105is produced. In order to simulate this effect, the strobes are shadedwith the exception of the crossover area 1105. If the back projectionshad been weighted, an even better estimate of the position of the jammerwould have been obtained. Of course, for a single jammer, LMS rangingcould have been used to obtain a comparable estimate of jammer position.

However, when the second jammer is added, it can be seen from FIG. 12that the jamming strobes 1102, 1103, 1104, 1202 and 1204 areautomatically identified with the correct jammers. That is, 1102, 1103and 1104 are associated with the jammer at 1105, and strobes 1103,1202and 1204 are associated with the jammer at 1205. The final display isbrightest only at the positions of the two jammers 1105 and 1205. Otherambiguous positions that correspond to potential jammers form an imagethat is considerably less bright than the true position. Of course, themore back projections there are, the more accurate this technique is. Inthe original CAT X-ray technique, a continuous set of back projectionsfrom all aspect angles is used to generate an excellent image of acompletely distributed object.

As noted, the use of the state of the art CAT X-ray technique provides asolution for stationary jammers, but unfortunately, in its present formfails to provide a solution for moving jammers, which a most commonproblem, encountered regularly with airborne jammers.

SUMMARY

It is an object of the present invention to provide a completely passiveranging system where the ranging system and the emitting target are onindependent moving platforms.

It is an object of the present invention to provide a ranging systemcapable of determining the range to an emitting target as well as targetvelocity with angle of arrival of a jammer strobe being the onlyinformation obtained from the target.

It is an object of the present invention to provide a target rangingsystem capable of operating in a high density environment.

In a typical case, the system of the present invention accepts as inputsthe angle of arrival of strobes of electromagnetic energy such as jammerstrobes from a target aircraft and stores this information along withthe time of arrival of the strobe and the cross range position of thesurveillance aircraft.

The data from three or more consecutive strobes is used to compute threeor more planes in which both the target and receiving aircraft arelocated at the time of the strobes. The intersection of these planesprovides the range and velocity of the target aircraft. A specificembodiment for implementing this system is presented. This embodiment iscapable of determining target range and velocity from received angle ofarrival data only. In addition, the embodiment includes a visualpresentation to enhance target identification through the use ofoperator interpretation, which is especially advantageous in highdensity environments.

BRIEF DESCRIPTION OF THE FIGURES

FIG. 1A is a diagram showing the flight path of a surveillance and atarget vehicle.

FIG. 1B is a perspective view of the paths of FIG. 1.

FIG. 2 is a first construction which presents vehicle velocity on theflight paths of FIG. 1B.

FIG. 3 is a second construction which presents vehicle velocity on theflight paths of FIG. 1B.

FIG. 4 is a third construction which presents vehicle velocity on theflight paths of FIG. 1B.

FIG. 5 is an expansion of a portion of the construction of FIG. 4.

FIG. 6 is a block diagram of a specific embodiment of the presentinvention.

FIG. 7 is a diagram showing the flight paths of a surveillance and atarget aircraft.

FIG. 8 is a diagram showing the flight paths of a surveillance aircraftand two targets.

FIG. 9 is a diagram showing the flight path of a surveillance aircraftand a single fixed target.

FIG. 10 is a diagram showing the flight path of a surveillance aircraftand two fixed targets.

FIG. 11 is a cathode-ray tube representation of a flight path of asurveillance aircraft and a fixed target.

FIG. 12 is a cathode-ray tube representation of a flight path of asurveillance aircraft and two fixed targets.

DETAILED DESCRIPTION OF THE INVENTION

The system technique of the present invention is used to solve theproblem of locating moving targets when the surveillance vehicle is alsoin motion and only angle of arrival information is available. As astarting point, reference is made to the traditional approach used for asingle moving jammer as illustrated in FIG. 1A. Note that this is only atwo dimensional Figure. In order to describe the approach of the presentinvention, an additional dimension which corresponds to jammer velocityis required. Hence, below the first illustration shown in FIG. 1A, aperspective version is shown in FIG. 1B in which a Z axis dimension hasbeen added to provide a means of representing velocity.

FIG. 1A shows a first flight path 101 of a target aircraft carrying anemitter such as a jammer, a second flight path 102 of an intercept orsurveillance aircraft, first, second and third segment of thesurveillance flight path designated by drawing numeral 103, 104 and 105,respectively, a corresponding first, second and third segment of thejammer flight path designated by drawing numerals 109, 110 and 111,respectively, and strobes connecting the respective centers of thefirst, second and third segments of the two flight paths, designated bydrawing numerals 106, 107 and 108. To aid in distinguishing the threedifferent flight path segments and their respective strobes, a dottedline has been used for the first, a dashed line for the second and asolid line for the third.

FIG. 1B illustrates two flight paths and their associated strobes whichare similar to those shown in FIG. 1A. The elements in FIG. 1B thatcorrespond to the elements in FIG. 1A are designated with identicaldrawing numerals, however, the letter "A" has been added to each drawingnumeral in FIG. 1B to identify the Figure from which these elementsoriginate. FIG. 1B also includes a coordinate axis in which the X, Y andZ axes are designated by drawing numerals 112A, 113A, and 114A,respectively.

In FIGS. 1A and 1B, the strobes represent the direction of arrival of asignal transmitted from the target aircraft during each segment of theflight paths. The target and surveillance aircrafts are considered ashaving passed through and completed each of the corresponding segmentsof the respective flight paths simultaneously. The flight paths shown inFIG. 1B are considered as lying in the X-Y plane. The Z direction inthis Figure is reserved for a representation of tangential velocity ofthe target aircraft as will be apparent from the description ofsubsequent Figures.

In order to determine the estimated range and velocity of the targetaircraft, it is necessary to construct a three dimensional diagram, asshown in FIG. 2. In this Figure, the Z axis 214 or "up" direction isused to represent the tangential component of the emitting aircraft'svelocity. The X axis and the Y axis are denoted by drawing numerals 212and 213, respectively.

Beginning with the dashed strobe 207, a planar surface of arbitraryheight is erected in the Z direction. Vertical lines 207A and 207B andparallel lines 207 and 207C define this surface. The time at which theposition and velocity of the emitting aircraft is estimated is that atwhich the dashed strobe 207 occurred. In FIG. 2, this is approximatelythe time of the midpoint of the total flight paths and also correspondsto the midpoint of the dashed flight paths.

A tilted planar surface, which includes as one edge the dotted strobe206, is erected next. This planar surface also includes edges 206A, B,and C and extends in the Z direction the same distance as the dashedplane. However, it is tilted in the Y direction 213 by an angle whosetangent is proportional to the time difference elapsed between thecollection of the dotted data and the dashed data (dashed time minusdotted time).

The construction is continued in FIG. 3. This Figure is virtuallyidentical to FIG. 2, with the exception of the four lines designated bydrawing numerals 301 through 305. All of the drawing numerals which werepreviously shown in FIG. 2 have been deleted in this Figure to avoidcluttering. In this construction, the intersection of the dotted planewith the dashed plane is now determined. This is done by extending thedotted plane in the X direction at its left and right edges. The leftedge 303 of the dotted plane is moved back to the position indicated byline 304 where the X coordinate of the left edge of the dotted planeequals the X coordinate of the left edge of the dashed plane. Similarlythe right edge 301 of the dotted plane is moved to the right to theposition indicated by drawing numeral 302 where its X component equalsthe X component of the right edge of the dashed plane. Then theintersection of the left edge of the dotted plane with the left edge ofthe dashed plane corresponds to one point that is on a line whichindicates the intersection of the two planes. The intersection of theright edges of these two planes is a second point on the intersectionline designated by drawing numeral 305. For purposes of visual andsource identification, line 305 is formed of alternate dots and dashes.

A similar construction is made for a solid line plane in FIG. 4. Rightedge 402, top edge 405 and left edge 404 are added to solid line 108A toform the solid line plane. This plane is tilted at an angle whosetangent is proportional to the time elapsed between the collection ofthe solid data and the dashed data (solid time minus dashed time). Theconstant of proportionality is the same as was used in determinig thetilt angle of the dotted plane. The left and right edges 404 and 402 ofthe solid line plane are moved inward towards the center of the plane toform new edges 403 and 401 respectively which have the same X value asdashed edges 207B and 207A respectively.

The intersection of the dashed plane with the solid plane is indicatedby line 406 which is formed of long dashes alternated with short dashes.Since line 305 lies in the dashed plane and line 406 lies in the sameplane, these lines will intersect. This intersection is shown in FIG. 5.

FIG. 5 is an enlarged drawing of the right hand portion of FIG. 4 inwhich lines 305 and 406 have been extended to intersect at point 501.Point 501 is projected on the X-Y plane as point 503 by line 502. Theheight of line 502 is proportional to the velocity of the target at thereference time of interest. Point 503 represents the position of thetarget at the reference time of interest.

If there are more than three observations, then all the planes may notintersect in one point due to angle measurement errors. To accommodatethis potential error, each back projection plane is thickened into awedge (such as the wedges shown in FIGS. 11 and 12) by an amount equalto the expected uncertainty of the angle of arrival information due toantenna errors or non-constancy of jammer motion. Then, each backprojection wedge is assigned an intensity variation that is brightest atthe central back projection plane, and diminishes towards the edges ofthe wedge. The most likely intersection point is found by summing theintensities of the back projection wedges.

It will be appreciated that this approach is a graphical method ofsearching for jammer tangential velocity. Furthermore, if there is morethan one jammer, it can be seen that such a processor has the advantageof being completely linear--that is, superposition holds independent ofthe number of strobes or jammers. In addition, the jamming strobes areautomatically associated with the correct jammers in a manner similar tothat described for fixed target CAT ranging.

A specific embodiment implementing this technique is illustrated in FIG.6. In this embodiment, the three dimensional construction describedpreviously, is implemented via a pair of cathode-ray tube displaymonitors deflected in an X-Y fashion. This pair of monitors is viewedstereoptically to create a visual impression of a three dimensionalprocessing volume.

Inputs for the implementation are the angle of arrival strobes obtainedby the surveillance receiver or other sensor. For the example of where aradar receiver aboard a surveillance aircraft receives externallygenerated jamming signals, each revolution of the surveillance radarantenna would result in a number of detected strobes and the angles ofarrival of the strobes would be noted by the operator. Thus the strobeangle of arrival for each particular strobe and the surveillanceaircraft position at the time the strobe is received are entered asprimary inputs at the input port 604. In addition, if the display is tobe offset from zero range (for example if the targets are expected to beat no closer range than say 100 miles), then the minimum display rangeis also entered as a constant in the minimum display input port 601.Furthermore, each time a strobe is detected and entered into the strobeinputs 608A and 608B of the Figure, a store trigger must be provided asfor example manually by way of a push button so that the current data isstored and the inputs are made available for entry of the next strobe.

The strobe angle is assumed to be entered at input 602 in the form of apolar angle relative to north where north is used for referencepurposes. An arc tangent function of this angle is obtained in functiongenerator 603 for convenience in processing. The arc tangent slope isthen multiplied in multiplier 605 by the minimum display range set as aninput 601. If the minimum display range does not change significantlyover the time required to process the data(perhaps a few minutes) thenthe multiplication can be performed most simply by using a potentiometeras shown in function generator 605. In this case, the slope is theelectrical input to the potentiometer and the minimum display range isset by the operator by turning the control. The output of thepotentiometer is then added in adder 606 to the instantaneous sensorcross range position also input by the operator. This results in thestrobe line being defined by a slope (m) and an intercept (b); that is,in the form Y=mX+b.

Of course in modern surveillance radar systems navigation information isoften already in rectangular form. Hence, the arc tangent function withits associated multiplier and adder is shown as an option. The strobeline position might easily be entered into the storage-replay unit 627directly in the rectangular form of slope and intercept.

In any event, when these values are available for a particular strobe,the stored trigger from 608B causes the values to be recorded in memoryin the store-replay unit 627. This may be done most conveniently indigital form, using a shift register, an A to D, and a D to A converter.The data quantity to be stored depends upon the number of strobesobtained per revolution of the radar antenna and the number ofrevolutions per data run. Typically, a dozen or so strobes perrevolution might be expected and about 100 revolutions of the antennaare required to obtain sufficient data for accurate ranging. Thus, inthe order of 1200 slope/intercept number-pairs must be stored over aninterval of perhaps several minutes.

After data taking is completed, the data is replayed into a processor ata much higher rate than it was stored. In the processor, a replaytrigger is provided by a trigger generator 611 operating at a high pulserepetition frequency (perhaps 10 MHz) and a divider 610 which dividesthe trigger frequency by a factor (N) equal to the number of resolvablevelocity planes that it is desired to synthesize. The signal deriveddirectly from the generator and that from divider are the fundamentalsignals forming the raster for the cathode-ray tubes 624 and 625(through X and Y deflection amplifiers 623, 619 and 615, 618).

The fast trigger is used to initiate by way of line 626 a fast saw-toothgenerator 620 which provides linear (with time) deflections of the twoCRT tubes 624 and 625 in the X direction. After N deflections in thehorizontal or X direction have been performed the replay trigger is alsoapplied to a slow saw-tooth generator 609. Thus, during the fastsaw-tooth repetition time interval, the output of the slow saw-toothgenerator can be considered to be a slowly moving or even a constantvoltage. The "constant" voltage is then proportional to the particularvelocity being processed for each fast trigger. The purpose of thiscircuitry is to cause lines having the form Y=mX+b to separate in thehorizontal plane in order to give the operator the impression that thelines are moving away from the operator.

For the duration of the slow saw-tooth generator sweep (which includesmany, (N), fast saw-tooth generator sweeps) only one of the previouslystored strobe slope and intercept line value pairs will be presented atthe output lines of the storage and replay unit. These constant slowsaw-tooth voltages are applied to a multiplier 616 and an adder 617 toproduce from the fast saw-tooth X-deflection signal, an attenuated andshifted fast saw-tooth Y-deflection signal. If this Y-deflection signalwere applied without modification to the Y-deflection amplifiers, theresult would be a single line on both the left and right monitor with aslope and intercept equal to the voltage values m and b respectively.These lines would of course be identical and when viewedstereoscopically would appear to be in the plane of the TV screen.

However, the output of the adder 617 is not applied directly to the Ydeflection amplifiers but instead is offset by adding (for the leftmonitor in adder 613) or subtracting (for the right monitor insubtractor 614) the approximately constant voltage appearing at theoutput of the slow saw-tooth generator. Thus the sweeping of the slowsaw-tooth generator causes the apparent third dimensional position ofthe strobe line to move off the phosphor plane of the CRT display. Aslong as the slow saw-tooth generator frequency (that is the replaytrigger PRF 608B)is rapid compared with the response time of the eye,the resulting display will appear as a plane in three dimensional spaceas described in the previous discussion concerning the rangingconstructions in FIGS. 1 through 5.

The next replay trigger calls up the next strobe slope and interceptvalues and the process is repeated for that strobe. This procedure isrepeated until all of the strobes detected for all of the antennarevolutions of the radar system have been displayed.

Typically, the fast trigger would be generated at a 10 megacycle rateand in the order of 100 velocity planes would be synthesized. This wouldresult in a replay trigger PRF in the order of 100 kilocycles (if N wereequal to 100). If there are 1200 strobe lines stored in the storagereplay device all data will then be replayed in 12 milliseconds. Theprocess may then be repeated, replaying the same data repetitively at an80 hertz rate (1/12 ms). This 80 hertz repetition frequency of theentire display results in a flicker-free three dimensional presentationof the entire data-set. The predicted target position and velocityappears brightest because the display monitors spend more time tracingthrough these positions than they do in tracing through other positionsthat do not contain targets.

Having described my invention, I claim:
 1. Apparatus for determining thelocation and velocity of a target from the angle of strobes emitted bythe target, the time of the strobes, and the cross-range position of thesensor at the time of each strobe, comprising:(a) a first cathode-raytube, (b) a second cathode-ray tube, (c) a first Y deflection amplifierconnected to the first cathode-ray tube to control the Y deflection ofthe first tube, (d) a second Y deflection amplifier connected to thesecond cathode-ray tube to control the Y deflection of second tube, (e)a first X deflection amplifier connected to the first cathode-ray tubeto control the X deflection of the first tube, (f) a second X deflectionamplifier connected to the second tube to control the X deflection ofthe second tube, (g) a store-replay unit means for accepting thefollowing four input: a trigger to store each strobe, the arc tangent ofthe strobe angle, and a function equal to a minimum display rangedesired multiplied by the arc tangent of the strobe angle, all added tothe sensor cross range position, and the time of the strobe said storereplay unit means storing and processing such inputs as delineated inparagraph (l), (h) a trigger generator, (i) a fast saw-tooth generator,receiving as an input the trigger from the trigger generator to initiateeach saw-tooth pulse, the output saw-tooth being supplied to the Xdeflection amplifiers to provide a sweep of the cathode-ray tubes, (j) adivide-by-N-counter receiving as an input the trigger from the triggergenerator to produce a lower frequency trigger output at a frequencyequal to the trigger generator frequency divided by N, the lowerfrequency trigger output being in synchronism with the trigger from thetrigger generator, (k) a slow saw-tooth generator receiving the slowtrigger output of the divide-by-N-counter to initiate each saw-toothwave, (l) means for coupling the slow trigger output from thedivide-by-N-counter to the store replay unit means to cause the storereplay unit means to provide the following outputs: a time of strobe,the slope of the strobe line (m) and the intercept of the strobe line(b), derived from the minimum display range, the cross range positionand the arc tangent of the strobe angle as delineated in paragraph (g),(m) a first multiplier receiving as inputs the output of the fastsaw-tooth generator and the slope (m), (n) a first adder receiving asinputs the output of the first multiplier and the strobe intercept (b),(o) a second multiplier accepting as inputs the time from the storereplay unit means and the output of the slow saw-tooth generator, (p) asecond adder accepting as inputs the output of the first adder and theoutput of the second multiplier, (q) a third adder accepting as inputsthe output of the second adder and the output of the slow saw-toothgenerator, and supplying its output to the first Y-deflection amplifierfor deflecting the first cathode-ray tube in the Y direction, (r) afirst subtracter accepting as its first input the output of the secondadder and as its second input the output of the slow saw-toothgenerator, the second input being subtracted from the first in thesubtracter to produce a difference output which is supplied to thesecond Y-deflection amplifier for deflecting the second cathode-ray tubein the Y direction, and (s) means for coupling the output from the fastsaw-tooth generator to both the first and second X-deflection amplifiersto deflect the first and second cathode tubes in the X-direction.
 2. Asystem for determining the location and velocity of a target by a sensorusing the angle of strobes received from the target, the time ofoccurrence of the strobes and the cross range position of the sensor atthe times of the strobes, comprising the steps of:(a) presenting arepresentation of a first plane, said first plane encompassing the pathsof the target and the sensor during the periods of the strobes, saidfirst plane including all the strobes, (b) plotting a representation ofthe positions of the sensor at the time of each strobe in said firstplane, (c) plotting a representation of a first series of lines in saidfirst plane through the position of the sensor at the angle of thestrobe received at each of the position of the sensor, said first seriesof lines being referred to as strobe lines, (d) selecting arepresentation of the position of the sensor and the target at midrangeand designating them as the reference positions and their time ofoccurrence as the reference time, (e) erecting a representation of asecond plane orthogonal to the first, said second plane including thestrobe line passing through the reference position of the sensor, andsaid second plane being referred to as the reference plane, (f) erectinga representation of a first series of plane through selected positionsof the sensor and the corresponding strobe lines received at thesepositions, the selected positions including those occurring prior to aswell as after the occurrance of the reference position, each of theplanes in this first series being tilted towards the reference plane atangles which are proportional to the time elapsed between the time ofoccurrence of the sensor position through which a plane in the firstseries passes and the time of occurrence of the sensor positions throughwhich the reference plane passes, (g) generating a representation of asecond series of lines which are formed by the intersections of thefirst series of planes with the reference plane, (h) drawing arepresentation of the point of intersection of the second series oflines, (i) generating a representation of a line orthogonal to the firstplane which passed through the point of intersection of the secondseries of lines, (j) measuring the position of the point through whichthe orthogonal line of step (i) passes in the first plane to determinethe location of the target at the reference time, and (k) measuring thelength of the orthogonal line in subparagraph (i) to determine thevelocity of the target at the reference time.
 3. A system as describedin claim 2, further comprising the steps of:(a) expanding said firstseries of planes into wedges, the plane about which a wedge is formedbeing referred to as a central plane, the apex of a particular wedgebeing formed along a line passing through the selected positions of thesensors through which the particular central plane passes, (b)illuminating each wedge with varying intensity, wherein the brightestareas is the central plane about which a particular wedge is formed, thebrightness of the wedge having a gradient towards less brightness intraversing the area orthogonally away from the central plane of theparticular wedge and towards the edges of that wedge, (c) locating thebrightest point at the intersection of the wedges produced from thefirst series of planes, (d) generating a representation of a lineorthogonal to the first plane which passes through the point of step(c), and (e) measuring the position of the point through which theorthogonal line of step (c) passes to determine the location of thetarget at the reference time.